Respuesta :
Given:
x - 2y = 11
2x + y = 19
To solve using elimination method, we have:
• Step 1:
Multiply equation 1 by 2, then multiply equation 2 by 1.
x - 2y = 11 ....................x2
2x + y = 19...................x1
2x - 4y = 22
2x + y = 19
• Step 2:
Now, subtract both equations:
[tex]\begin{gathered} 2x-4y=22 \\ -2x\text{ +y = 19} \\ _{----------} \\ \text{ -5y = }3 \end{gathered}[/tex]• Divide both sides by -5:
Replace y with -3/5 in any of the equations to find x.
Let's take equation 2:
[tex]\begin{gathered} 2x\text{ -}\frac{3}{5}=19 \\ \end{gathered}[/tex]Multiply through by 5 to eliminate the fraction:
[tex]\begin{gathered} 2x(5)-\frac{3}{5}\ast5=19(5) \\ \\ 10x-3=95 \end{gathered}[/tex]Add 3 to both sides:
[tex]\begin{gathered} 10x-3+3=95+3 \\ \\ 10x\text{ = 98} \end{gathered}[/tex]Divide both sides by 10:
[tex]\begin{gathered} \frac{10x}{10}=\frac{98}{10} \\ \\ x\text{ =}\frac{49}{5} \end{gathered}[/tex][tex]x\text{ = }\frac{49}{5},\text{ and y=-}\frac{3}{5}[/tex]ANSWER:
[tex]\text{(}\frac{49}{5},\text{ -}\frac{3}{5})[/tex]